In this article, we would be implementing the Binary Search Tree data structure in Javascript. A tree is a collection of nodes connected by some edges. A tree is a non linear data structure. A Binary Search tree is a binary tree in which nodes that have lesser value are stored on the left while the nodes with a higher value are stored at the right.
Now let’s see an example of a Binary Search Tree node:
Javascript
// Node classclass Node{ constructor(data) { this.data = data; this.left = null; this.right = null; }} |
As in the above code snippet we define a node class having three property data, left and right, Left and right are pointers to the left and right node in a Binary Search Tree. Data is initialized with data which is passed when object for this node is created and left and right is set to null.
Now let’s see an example of a Binary Search Tree class.
Javascript
// Binary Search tree classclass BinarySearchTree{ constructor() { // root of a binary search tree this.root = null; } // function to be implemented // insert(data) // remove(data) // Helper function // findMinNode() // getRootNode() // inorder(node) // preorder(node) // postorder(node) // search(node, data)} |
The above example shows a framework of a Binary Search tree class, which contains a private variable root which holds the root of a tree, it is initialized to null.
Now lets implement each of this function:
1. insert(data) – It inserts a new node in a tree with a value data
Javascript
// helper method which creates a new node to // be inserted and calls insertNodeinsert(data){ // Creating a node and initialising // with data var newNode = new Node(data); // root is null then node will // be added to the tree and made root. if(this.root === null) this.root = newNode; else // find the correct position in the // tree and add the node this.insertNode(this.root, newNode);}// Method to insert a node in a tree// it moves over the tree to find the location// to insert a node with a given data insertNode(node, newNode){ // if the data is less than the node // data move left of the tree if(newNode.data < node.data) { // if left is null insert node here if(node.left === null) node.left = newNode; else // if left is not null recur until // null is found this.insertNode(node.left, newNode); } // if the data is more than the node // data move right of the tree else { // if right is null insert node here if(node.right === null) node.right = newNode; else // if right is not null recur until // null is found this.insertNode(node.right,newNode); }} |
In the above code we have two methods insert(data) and insertNode(node, newNode). Let’s understand them one by one:-
- insert(data) – It creates a new node with a value data, if the tree is empty it add this node to a tree and make it a root, otherwise it calls insert(node, data).
- insert(node, data) – It compares the given data with the data of the current node and moves left or right accordingly and recur until it finds a correct node with a null value where new node can be added.
2.remove(data) – This function removes a node with a given data.
Javascript
// helper method that calls the // removeNode with a given dataremove(data){ // root is re-initialized with // root of a modified tree. this.root = this.removeNode(this.root, data);}// Method to remove node with a // given data// it recur over the tree to find the// data and removes itremoveNode(node, key){ // if the root is null then tree is // empty if(node === null) return null; // if data to be delete is less than // roots data then move to left subtree else if(key < node.data) { node.left = this.removeNode(node.left, key); return node; } // if data to be delete is greater than // roots data then move to right subtree else if(key > node.data) { node.right = this.removeNode(node.right, key); return node; } // if data is similar to the root's data // then delete this node else { // deleting node with no children if(node.left === null && node.right === null) { node = null; return node; } // deleting node with one children if(node.left === null) { node = node.right; return node; } else if(node.right === null) { node = node.left; return node; } // Deleting node with two children // minimum node of the right subtree // is stored in aux var aux = this.findMinNode(node.right); node.data = aux.data; node.right = this.removeNode(node.right, aux.data); return node; }} |
In the above code we have two methods remove(data) and removeNode(node, data), let understand them one by one:
- remove(data) – It is helper methods which call removeNode by passing root node and given data and updates the root of the tree with the value returned by the function
- removeNode(node, data) – It searches for a node with a given data and then perform certain steps to delete it.
- Deleting the leaf node – As leaf node does not have any children, hence they can be easily removed and null is returned to the parent node
- Deleting a node with one child – If a node has a left child, then we update the pointer of the parent node to the left child of the node to be deleted and similarly, if a node have a right child then we update the pointer of the parent node to the right child of the node to be deleted
- Deleting a node with two children – In order to delete a node with two children we find the node with minimum value in its right subtree and replace this node with the minimum valued node and remove the minimum valued node from the tree
Now Lets understand different ways of traversing a Binary Search Tree.
inorder(node) – It performs inorder traversal of a tree starting from a given node
Algorithm for inorder:
Traverse the left subtree i.e perform inorder on left subtreeVisit the rootTraverse the right subtree i.e perform inorder on right subtree
Javascript
// Performs inorder traversal of a treeinorder(node){ if(node !== null) { this.inorder(node.left); console.log(node.data); this.inorder(node.right); }} |
1. preorder(node) – It performs preorder traversal of a tree starting from a given node.
Algorithm for preorder:
Visit the rootTraverse the left subtree i.e perform preorder on left subtreeTraverse the right subtree i.e perform preorder on right subtree
Javascript
// Performs preorder traversal of a tree preorder(node){ if(node !== null) { console.log(node.data); this.preorder(node.left); this.preorder(node.right); }} |
2. postorder(node) – It performs postorder traversal of a tree starting from a given node.
Algorithm for postorder:
Traverse the left subtree i.e perform postorder on left subtreeTraverse the right subtree i.e perform postorder on right subtreeVisit the root
Javascript
// Performs postorder traversal of a treepostorder(node){ if(node !== null) { this.postorder(node.left); this.postorder(node.right); console.log(node.data); }} |
Helper Methods
Let’s declare some helper method which is useful while working with Binary Search Tree.
1. findMinNode(node) – It searches for a node with a minimum value starting from node.
Javascript
// finds the minimum node in tree// searching starts from given nodefindMinNode(node){ // if left of a node is null // then it must be minimum node if(node.left === null) return node; else return this.findMinNode(node.left);} |
As seen in the above method we start from a node and keep moving to the left subtree until we find a node whose left child is null, once we find such node we return it.
2. getRootNode() – It returns the root node of a tree.
Javascript
// returns root of the treegetRootNode(){ return this.root;} |
3. search(data) – It searches the node with a value data in the entire tree.
Javascript
// search for a node with given datasearch(node, data){ // if trees is empty return null if(node === null) return null; // if data is less than node's data // move left else if(data < node.data) return this.search(node.left, data); // if data is more than node's data // move right else if(data > node.data) return this.search(node.right, data); // if data is equal to the node data // return node else return node;} |
Note : Different helper method can be declared in the BinarySearchTree class as per the requirement.
Implementation:
Now lets use the BinarySearchTree class and its different methods described above.
Javascript
// create an object for the BinarySearchTreevar BST = new BinarySearchTree();// Inserting nodes to the BinarySearchTreeBST.insert(15);BST.insert(25);BST.insert(10);BST.insert(7);BST.insert(22);BST.insert(17);BST.insert(13);BST.insert(5);BST.insert(9);BST.insert(27); // 15// / \// 10 25// / \ / \// 7 13 22 27// / \ /// 5 9 17 var root = BST.getRootNode(); // prints 5 7 9 10 13 15 17 22 25 27BST.inorder(root); // Removing node with no children BST.remove(5); // 15// / \// 10 25// / \ / \// 7 13 22 27// \ /// 9 17 var root = BST.getRootNode(); // prints 7 9 10 13 15 17 22 25 27BST.inorder(root); // Removing node with one child BST.remove(7); // 15// / \// 10 25// / \ / \// 9 13 22 27// /// 17 var root = BST.getRootNode();// prints 9 10 13 15 17 22 25 27BST.inorder(root); // Removing node with two children BST.remove(15); // 17// / \// 10 25// / \ / \// 9 13 22 27var root = BST.getRootNode();console.log("inorder traversal");// prints 9 10 13 17 22 25 27BST.inorder(root); console.log("postorder traversal");BST.postorder(root);console.log("preorder traversal");BST.preorder(root); |
For more on binary trees, please refer to the following article: Binary tree Data Structure
This article is contributed by Sumit Ghosh. If you like neveropen and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the neveropen main page and help other Geeks.
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